The following text is written under the assumption that the
reader has thorough knowledge about the relation between gas fractions and
partial pressures as well as basic knowledge in rebreather design. Also, Nitrox
concepts like MOD and EAD are assumed to be familiar to the reader. A few
differential equations and Laplace transforms appear but it is not necessary to
understand them in order to understand constant mass flow semi-closed rebreather
(CMF SCR).

The text presents the general behaviour of the breathing
gases in a CMF SCR as well as two ways of determining the fresh gas flow and
fresh gas mixture in a CMF SCR, one based on a known fresh gas mixture and one
based on a planned diving depth.

Note that different
authors and different manufacturers in general use their own values for the
maximum and minimum oxygen uptakes as well as the safety factor when
dimensioning the flows. It is up to the reader to use ****his/hers*** knowledge
and common senseto determine
whether he/she believes that the estimates used are relevant or not!

/*
begin US lawyer BS */
Please note: The following pages most likely contains a lot of errors and
misunderstanding that could mislead you and make you build and or use dangerous
devices that might get you, or someone you like, killed. If you believe in any
of the information found on these pages it is your own fault! The author
assumes no responsibility whatsoever neither for errors in the text nor for
possible mishaps because a reader misreads or misinterprets the information
contained herein./* end US Lawyer BS
*/

The oxygen uptake (or oxygen consumption), , of a diver vary with how hard the diver is working.

Oxygen uptake

Equivalent work

0.3 [L/min]

The oxygen uptake at rest for an average 75 kg man

0,8 [L/min]

The oxygen uptake when swimming at about 0.5 knots.

1.3 [L/min]

The average long time consumption of a fit hard working
diver.

2.0 [L/min]

The maximum oxygen uptake used by a diver*

* Note that a very fit diver can, in
extreme cases, consume more than 4 [L/min] swimming in water but oxygen
consumptions as high as 2 [L/min] are rarely seen in real dives.

The reader that really is interested in the relevant
physiology is referred to: Bennet and Elliot, The Physiology and Medicine of
Diving, Saunders 1993, ISBN 0-7020-1589-X, especially chapter 5 respiration and
exertion.

In a semi closed rebreather the
oxygen fraction in the breathing circuit, FO2, depends on the
diver's oxygen uptake, VO2, and the added flow of fresh gas, Qmix,
and fresh gas oxygen fraction (i.e. percentage), Fmix, of the fresh
gas.

The time constant, i.e. how fast the oxygen fraction change,
of the semi-closed rebreather depends on the flow venting the breathing circuit
and the gas volume (as measured in normal litres, i.e. surface equivalent
volume!) of the complete breathing circuit, i.e. including divers lungs,
canister, tubes, and counter lungs.. The time constant can be seen as the
inverse of the exponent in the right hand part of the Eq. D.

Eq. F

The time constant, t, i.e. the time it takes
for the system to change, is significant, see the figure below. The time
constant is the time needed for a system that sees a rapid (i.e. a step) change
to reach 63% if the final (i.e. steady state) value. About 3 time constants is
needed for the system to reach within 1% of the steady state value.

Figure 2. The time constants for a constant mass flow semi-closed
rebreather. The fresh gas flows are from the Draeger Dolphin manual for the
respective fresh gases. The oxygen consumption is assumed to be 1.3 [L/min] and
the total loop volume 12 liters.

Figure 3. An illustration of the rate of change in oxygen fraction in a
breathing circuit at different depths. The starting fraction is 40%, the total
volume of the circuit is 12L, the oxygen uptake of the diver is 1.3 L/min, the
fresh gas mixture is 40%, and the fresh gas flow is 10.3 L/min. The steady
state oxygen fraction in the breathing circuit is 31.4%.

The deeper the CMF SCR rebreather is dived, the
slower the oxygen fraction changes.

In practise the result is that a semi-closed rebreather that
is dived from the surface straight down to 50m and staying there for 10 min
exposure time will not have reached the steady state oxygen fraction value when
leaving the bottom!

For a SCR with a fresh gas flow of 12 [L/min], a fresh gas
oxygen fraction of 32.5%, and an oxygen uptake of 1,3 [L/min], the fraction in
the circuit will be about 25% when leaving the bottom, see simulation in the
graph below.

Figure 4. Simulation of a 10 min dive to 50 m with a CMF SCR running 32.5%
at 12 L/min. The oxygen uptake is 1.3L/min. Ascent and descent rates 10m/min.
Note the dropping in FO2 suring ascent due to the increased loss
(i.e. dumping) of oxygen.

Note:
The rate of change in oxygen fraction in a Closed Circuit Rebreather, CCR, does
_NOT_ behave like the CMF SCR!

where the (D+10)/10 is the absolute pressure
[bar] at a certain depth, D, [in meters]

Eq. H

By measuring the oxygen partial pressure in the breathing
loop, PO2meas
and calculating the oxygen fraction during the dive the oxygen uptake can be
estimated. _BUT_
there is a great risk of making a significant error here. If, for example, the
diver descends from the surface down to 10m and rests there while trying to
estimate his oxygen consumption his calculations will result in a underestimation
of his uptake since the rebreather has not yet reached steady state conditions
after the descent and bypass, see also the paragraph on time constants above.

If this erroneously low estimate of oxygen consumption is
used as a rationale for lowering the fresh gas flow in a CMF SCR there is a
true risk for a hypoxic surprise when working hard.

I
strongly advice againstusing the oxygen consumption calculated from
readings during a dive as a rationale for lowering the constant mass flow in
your rebreather!

There are (at least) two practices taught when
calculating the MOD for a CMF SCR. The first one uses the oxygen fraction of
the tank mixture like any OC Nitrox and the second calculates the oxygen
fraction in the loop with the diver at rest.

It is up
to the reader to choose which way he/she prefers. In practice the difference in
MOD calculated using the two methods is very small.

The maximum diving depth is determined by the
fact that the oxygen partial pressure in the breathing gas should not exceed a
certain limit. In cold waters a max PO2 of 1.4 [bars] is often used.

The highest oxygen fraction is seen
in the loop when the diver is at rest with low oxygen consumption; a VO2min
of 0.25 [L/min] is often used.

[bar]Eq. R

Or recalculated into depth in
meters:

[m]Eq.
S

Continuing the example using Eq.
R:

The oxygen fraction in the loop at
rest will be about 38% but note that the oxygen fraction in the loop immediately after a descent will
be higher than the steady state value partly because of the gas added
for volume compensation using the bypass.

Note
that different authors and different manufacturers use different estimated
values for the maximum and minimum oxygen uptakes as well as different safety
factors when dimensioning the flows. It is up to the reader to use his
knowledge and common sense to determine whether he/she believes that the
estimates and assumptions used below are relevant or not!

The necessary fresh gas flow, Q’mix, is
calculated so that the resulting (minimum) oxygen fraction, FO2, in
the breathing circuit will be 0.2 (i.e. 20%) when the divers’ oxygen uptake, VO2,
is 2 [L/min].

The fresh gas flow can be expressed in known variables as:

Eq. I

In order to determine the fresh
gas flow, Qmix, to use in the rebreather this value for the necessary
Q’mix should be increased with a safety factor, k, which
usually is in the range of 0.25 to 0.5 (i.e. 25% – 50%).

An example using an Fmix of 40% and a safety factor, k, of 0.25:

Using a 25% safety factor for a 40% mix the results indicate
that you should use 10 [L/min] of fresh gas flow, see table 1 below.

Fmix

[%]

Qmix (k=0)

[L/min]

Qmix
(k=0.25)

[L/min]

Qmix
(k=0.5)

[L/min]

32,5%

12,8

16,0

19,2

40,0%

8,0

10,0

12,0

50,0%

5,3

6,7

8,0

60,0%

4,0

5,0

6,0

80,0%

2,7

3,3

4,0

Table 1. Exemplifying the flow
calculated from known fresh gas oxygen concentration and with different safety
factors.